Fully Nonlinear Equations in Conformal Geometry
| MINI-COURSE IN GEOMETRIC PDE | |
| Topic: | Fully Nonlinear Equations in Conformal Geometry |
| Speaker: | Matt Gursky |
| Affiliation: | University of Notre Dame and Member, School of Mathematics |
| Date: | Tuesday, October 7 |
| Time/Room: | 1:30pm - 3:30pm/S-101 |
The goal of this course to provide an introduction to Monge-Ampere-type equations in conformal geometry and their applications.
The plan of the course is the following: After providing some background material in conformal geometry, I will describe the k-Yamabe problem, a fully nonlinear version of the Yamabe problem, and discuss the associated ellipticity condition and its geometric consequences.
Next, I will discuss a prori estimates, some basics of blow-up analysis, and entire solutions.
In order to reduce some of the technical issues involved, while providing an important example the geometric applications of these equations, I will then narrow my focus to the case of four dimensions, and sketch a proof of existence in this case. Finally, I will point out some geometric applications of the equations in four dimensions.